Well, one position is concerned with truth (e.g. "I'm a man") and one position is concerned with belief (e.g. "I believe you're a woman").

Being more concerned with what you believe about people over facts about them seems pretty selfish, but at this point if I haven't convinced you that perhaps people are a better judge of their identities than random strangers, I don't think I'm going to, and I agree that our positions are irreconcilable.

I'd point out, however, that your position doesn't really leave possibility to foster understanding between people who believe differently either; if I say I'm a man and somebody disagrees, they're ignoring the most primary of primary sources. That's not the position of somebody who's open to compromise; that's the position of somebody who's already made their decision and refuses to consider any other factor.